On the (Im)possibility of Basing Oblivious Transfer and Bit Commitment on Weakened Security Assumptions

Abstract

We consider the problem of basing Oblivious Transfer (OT)<br />and Bit Commitment (BC), with information theoretic security, on seemingly weaker primitives.We introduce a general model for describing such primitives, called Weak Generic Transfer (WGT). This model includes as important special cases Weak Oblivious Transfer (WOT), where both<br />the sender and receiver may learn too much about the other party's input, and a new, more realistic model of noisy channels, called unfair noisy channels. An unfair noisy channel has a known range of possible noise levels; protocols must work for any level within this range against adversaries who know the actual noise level. We give a precise characterization for when one can base OT on WOT. When the deviation of the WOT from the ideal is above a certain threshold, we show that no information-theoretic reductions from OT (even against passive adversaries) and BC exist; when the deviation is below this threshold, we give a reduction from OT (and hence BC) that is information-theoretically secure against active adversaries.<br />For unfair noisy channels we show a similar threshold phenomenon for bit commitment. If the upper bound on the noise is above a threshold (given as function of the lower bound) then no information-theoretic reduction from OT (even against passive adversaries) or BC exist; when it is below this threshold we give a reduction from BC. As a partial result, we give<br />a reduction from OT to UNC for smaller noise intervals.